DSL (Digital Subscriber Line) systems have become important within digital communication. One reason therefore is that DSL systems are capable of offering a large bandwidth for digital communication over existing telephone subscriber lines. Introduction of new applications and the need for services and variety in service offerings increase the need for broadband transmissions. Transmission rates steadily increase. The signal-to-noise-ratio (SNR) on communication lines has a strong influence on the performance of a broadband network and if it is not satisfactory, it restricts the use of such networks. Cross-talk is an important source of noise in DSL systems, for example ADSL and VDSL. Cross-talk adversely affects a signal when it passes through a transmission path and it may result in a corrupted signal which can be misinterpreted on the receiving side and translated to contain errors in the digital bit stream.
NEXT is defined as noise induced between lines at the near end of a link, which is defined as the end closest to the point of origin of the signal. FEXT is defined as noise induced onto an adjacent line by a transmitter on the near end of a first line onto the receiver at the far end of a second line. FEXT may for example be the result of imperfections in the cable.
Thus, high-speed communication over DSL can be severely limited by interference from adjacent metal, mostly copper, lines, e.g. twisted-pair lines, in an access network. This destructive cross-talk between neighbouring lines is considered as one of the most dominant impairments and consequently affects performance and poses a limit for improvements in performance.
Dynamic spectrum management (DSM) is one resource management approach to improve the transmission capacity of DSL lines. In DSM an algorithm is applied on a (copper) access cable binder, which consists of a number N of users, or lines, equipped with DSL transceivers. Each transceiver employs discrete multitone modulation (DMT) and operates over a twisted-pair line with K independent sub-channels or tones, in this document in the following mainly referred to as frequencies. Also the expression “lines” will mainly be used instead of “users”.
A received signal vector on tone (frequency) k can be modelled as: yk=Hk xk+ zk, for k=1,2, . . . , k wherein: xk=[x1k,x2k, . . . , xNk]T is the transmitted signal vector on frequency k for all N lines, yk=[y1k,y2k, . . . , yNk]T is the received signal vector on frequency k for all N lines, zk=[z1k,z2k, . . . , zNk]T is the additive noise vector on frequency k including the extrinsic network impairment, e.g. impulse noise, radio frequency interference (RFI), thermal noise and alien cross-talk.
Hk corresponds to an N×N matrix containing the channel transfer functions on frequency k, see FIG. 1B.
FIG. 1A illustrates DMT transmission for frequency k and produced FEXT and NEXT interference on a cable binder.
The channel matrix H in FIG. 1B characterizes the cable binder by representing both the direct transfer function and the FEXT/NEXT coupling transfer functions. It can be interpreted along the three dimensions N×N×K, i.e. the dimensions of the channel matrix.
Each channel vector hn,m=[hn,m1,hn,m2, . . . , hn,mK] represents the transfer function of the channel from a transmitter m to a receiver n over the frequency band (tones).
The DSM techniques implement power spectrum density (PSD) level optimization in order to assign a transmit PSD for each user within the DSL network to minimize cross-talk interference. The PSD assignment is conducted according to a set of predefined criteria and constraints, for example by maximizing user rates under power limitation, which can be one underlying basis or object of spectral management. Other objects or combinations of objects are possible.
The spectral management issue is commonly formulated as a maximization problem of a weighted-rate-sum, subject to a power constraint per user.
However, spectral management techniques in general, DSM techniques in particular, suffer from being complex (DSM level 2, as well as DSM level 3, Vectoring algorithms). DSM spectral management and vectoring is e.g. discussed in Dynamic Spectrum Management Technical Report (2007), ATIS Committee NIPP Pre-published document ATIS-PP-0600007. Several algorithms have been introduced for presenting a solution to the spectral management issue or problem referred to above. One of these algorithms is the Iterative Spectrum Balancing algorithm (ISB). ISB is for example described in “Iterative spectrum balancing for digital subscriber lines”, by R. Cendrillon and M. Moonen, in IEEE Transactions on Communications, May 2006. The ISB algorithm adopts an optimization process involving a high computational complexity. In order to determine the best PSD distribution for N users, (i.e. N lines), on K frequencies, the ISB will result in a complexity of O(PlevelKN2), i.e. Ordo(PlevelKN2), wherein Plevel indicates total number of possible power levels.
However, a typical metal or copper access cable normally consists of several cable binders grouped together and resulting in a DSL network containing several twisted-pair lines, for example 100 lines. Even if the copper access cables are manufactured in order to minimize cross-talk, among others through trying to keep a twisting between lines along the cable, there are many lines and since the DSM technique uses all lines, i.e. the total number of lines, it is immediately apparent that a considerable amount of computations have to be performed. It is also a drawback that, if a state of a line must be updated, e.g. the transmission PSD level changed, then all the other lines in the binder must be updated as well. The DSM algorithm solutions typically have a quadratic complexity in the number of lines N and a linear complexity in the number of frequencies or tones K. The ISB algorithm has the complexity O(PlevelKN2) as mentioned above.
Due to the computational complexity the deployment of DSM algorithms will be restricted, which is unfortunate. For example, a copper access network employing VDSL2 systems with K=4096 tones, a total of N=20 lines and Plevel=112 levels, would result in a highly complex problem using current algorithms as discussed in the state of the art.